Honors Pre-Calculus
Name________________________________
Quarter Three Review
Solve the problem.
1. Among a group of 71 investors, 25 owned shares of Stock A, 29 owned shares of Stock B, 38 owned shares of
Stock C, 14 owned shares of both Stock A and Stock B, 11 owned shares of Stock A and Stock C, 18 owned
shares of Stock B and Stock C, and 9 owned shares of all three. How many investors did not have shares in any
of the three? How many owned shares of either Stock A or Stock C but not Stock B?
2.
A spinner has six numbers (of equal probability) on it. Find the probability that if you spin it 10 times, you get
exactly 4 fives.
3.
From 8 students in a class, a group of 3 will be chosen to be in the math club. How many different groups are
possible?
4.
How many 4-digit numbers can be formed using the digits 1,2,3,4,5,6,7,8,9, and 0? No digit can be used more
than once.
5.
At a restaurant, there is a choice of 8 entrees, 7 side dishes, and 5 desserts. Your Mom says you can pick 2
entrees, 3 side dishes, and 2 desserts. How many different combinations of meals could you choose?
6.
From a deck of 52 cards, you select one card at random. What is the probability that it is either a club or a king?
Solve the right triangle.
7.
a  2.9 m,   43.0
Solve the problem.
8.
A building 180 feet tall casts a 40 foot long shadow. If a person stands at the end of the shadow and looks up to
the top of the building, what is the angle of the person’s eyes to the top of the building ? (Assume the person’s
eyes are 4 feet above ground level.)
9.
An airplane is sighted at the same time by two ground observers who are 4 miles apart (with the airplane between
them) and in line with the airplane. They report the angles of elevation as 12 and 20 . How high is the
airplane?
Find the missing parts of the triangle.
10.   28 20',   28 10', a  45.25
11.   127.3 , a  5.70, b  8.56
12. a  15, b  17, c  13
Solve the problem.
13. A pick-up truck is fitted with new tires which have a diameter of 44 inches. How fast will the pick-up truck be
moving when the wheels are rotating at 345 revolutions per minute? Express the answer in miles per hour
rounded to the nearest whole number.
A point on the terminal side of angle  is given. Find the exact value of the given trigonometric function.
14. (8, 7); find tan 
Find the exact value of the requested trigonometric function of  .
sin   
15.
Find
2
and tan   0
9
cos   _____
sec   _____
tan   _____
cot  _____
Write the equation of a sine function with the given characteristics.
16. Amplitude: 4
Period: 6
Phase Shift: left

6
A.
1 

y  4sin  3 x   
18 

C.


y  4sin  6 x  
6

1 
1

18 
3
1 
1
D. y  4sin  x   
18 
3
B. y  4sin  x 
Graph the following functions. Clearly label all key vertical and horizontal points. Find the amplitude, vertical
shift, phase shift, and period for each.
17.
y  2csc  3x     1 A =
VS =
PS =
Start =
End =
P=
18.
y  1cot  2x     3 A =
VS =
PS =
Start =
P=
End =
Prove the following.
19.
1  cot  1  cot    csc2   2cot 2 
Use trigonometric identities to find the exact value.
20.
sin 25 cos 35  cos 25 sin 35
Find the exact value of the expression.
21.

2
 1 
cos  sin 1    cos 1   
3
 3

Find the exact value of the expression under the given conditions.
22.
4
csc    , tan   0
3
Find cos  2 
Solve the equation for the interval 0, 2  .
23.
sin 2 x  cos 2 x  0
Use a calculator to solve the equation on the interval 0, 2  .
25.
tan   3.7
26.
cos 2x  2  cos 2 x
24. 2 cos 2   5cos   3  0
Answers:
1. 13, 29
2. .054
3. 56
4. 5040
5. 9800
6.
4
13
7.
  47.0 , b  2.704, c  3.965
8.
9.
77.195
.536 miles
18.
19. Proof
10.   123.5 , b  45.005, c  79.505
11. c  12.841,   20.676 ,   32.023
12.   47.431 ,   58.186 ,   74.381
13. 45 mph
14. 
7
(be able to find all six)
8
cos   
15.
tan  
16. D
17.
77
9
2
77
sec   
cot 
9
77
77
2
20.
3
2
5 4 2
9
1
22. 
8
 3 5 7
23.
, ,
,
4 4 4 4
2 4
24.
,
3 3
21.
25. 1.306, 4.448
26. .392, 2.748, 3.534, 5.890